For all the charming naivety of Laura Robson's faith in her raw teenage power, she is through to the third round of the Australian Open largely because she soaked up the fluctuating force of Petra Kvitova's serve and found new maturity at the end of three of the craziest sets she is ever likely to play.

While this shootout between two leftie gunslingers, the 18-year-old Briton on the rise and the former Wimbledon champion, was never going to be an exchange of subtleties, few would have predicted 92 unforced errors and 30 aces between them. It was, the winner said, "pretty ugly". However, the excitement and unevenness of the spectacle, which lasted exactly three hours and straddled midnight, ought not disguise the significance of the achievement.

To beat the eighth seed, albeit one in fitful form, four months after defeating Kim Clijsters and Li Na at the US Open marks a watershed in Robson's career. In the city where she was born and left with her parents when she was six, later to be nurtured as a British hope, she has arrived as a genuine contender, just a few days before her 19th birthday. Her development, which has come in a rush, echoes the breakthrough of another 18-year-old on the WTA Tour who reached the third round of consecutive slams: Melanie Oudin (whom she beat in the first round this week) when she announced her arrival in New York after Wimbledon in 2009.

In an era of maturity and ever more muscular tennis, that is a considerable feat. Robson is suited to the physicality of the modern game (although several times this match cried out for a sliver of subtlety) and there is a lot of tough tennis in front of her.

Expectations, always unreal, will rise further. She looks up to it. Caught in the vortex between risk and caution, she took a long time to contain her natural preference for a slugging match on her night-time debut in the Rod Laver Arena — it will not be her last appearance there – but did not shrink from the challenge.

"I knew it was going to be really, really tough," she said immediately afterwards. "I always struggle against lefties. Trying to return her serve was really hard, but when I got my returns going better and my confidence back, I managed to get myself into the match. I'm amazed so many people stayed to watch. I thought you were all going to leave after Federer. No tweeting now. I just need to sleep."

She had earned it, and there was a tangible wave of warmth from the crowd who had come to see Roger Federer win in the first match of the evening – easily against Nikolay Davydenko. They were glad they stayed for what was a remarkable, if wholly uneven, exhibition of kamikaze tennis.

As exciting as her crunching ground strokes can be, as intimidating her bullet serve, Robson will need to attend to her radar and composure if she is negotiate the equally precocious challenge of Sloane Stephens on Saturday.

There is little between them in talent and potential, although the young American's form has wavered here since she beat Robson in the first round in Hobart last week. It is a huge match for both of them. If she gets past Stephens, there is a golden opening against either the 42-year-old Kimiko Date-Krumm or the 21-year-old Serb Bojana Jovanovski, with Serena Williams waiting in the quarters. That is a mouth-watering incentive.

There will not have been many more disjointed matches in the tournament than this one. The tennis swung between breathtaking and awful, often in the same rally, with both players culpable. By the time Kvitova had thrashed down her sixth ace to take the first set after 38 minutes, she had double-faulted seven times, to Robson's four (two of them to open the match). Mis-hits did not just go out, they almost did not come back.

Both hit with stunning power off the ground, occasionally in the right direction, while their serving was worse than Manuel's in Fawlty Towers. A charitable interpretation was that there were eddying breezes down on court invisible from the stands, or someone had shrunk the court.

When Robson's first four serves failed to find the target, she feared the worst. A wayward forehand handed Kvitova three break points and a netted volley gifted her the opening game. Things could only get better. And worse again.

The unforced errors flowed at one every two minutes as both players continued to rip the cover off the ball, taking the most cursory notice of the net and white lines. The moths flitting around the arena had a better idea of where they were going.

Kvitova deserved to take the first set, but Robson seized on her 24th unforced error to get to a set apiece. It may have been messy, but it was not dull.

Kvitova found more serving juice in the third, but looked spent with two tired forehands from the baseline that gifted Robson the chance to serve for the match at 6-5. Familiar ball-toss jitters blunted the potency of her serve, though, and Kvitova was revived. Robson hit long twice, and they were back on equal terms.

When she served for the match a second time, Robson held her nerve like a veteran. She opened with an ace, her eighth. Her second was too strong for Kvitova: 30-0. Kvitova hit long: three match points. Another decent serve – and Kvitova's return floated wide. The elation was unconfined.

She will play better tennis than this, but the match and the occasion will not be quickly forgotten, by either participant or anyone present as the clock reached 12.30am.